基于图神经网络的导弹时序规划方法

doi:10.12305/j.issn.1001-506X.2025.03.18

摘要/Abstract

摘要：

多导弹协同编队作战已成为现代战争中打击关键目标的重要手段, 为应对瞬息万变的战场局势, 要求快速计算导弹发射时序, 使所有导弹在预定时间内准确完成打击任务。为解决多导弹协同发射时序规划问题, 基于图神经网络提出一种以导弹发射完成时间最小化为目标的整数线性规划模型, 设计出基于图神经网络模型的导弹发射顺序规划算法, 并基于节点采样和贪婪插入策略对导弹发射顺序进行局部优化, 可协助战场指挥员快速生成导弹发射时序方案。对20~200枚导弹协同发射实例进行验证分析。实验结果表明, 该模型和方法能有效解决多导弹协同发射时序规划问题。

关键词: 巡航导弹, 发射时序规划, 图神经网络, 局部优化

Abstract:

Multi-missile collaborative formation operation becomes an important means to strike key targets in modern war. In order to cope with the ever-changing battlefield situation, it is required to quickly calculate the missile launch temporal sequence, so that all missiles can accurately complete the strike task within the predetermined time. In order to solve the problem of temporal planning for multiple missile coordinated launch, an integer linear programming model with the goal of minimizing missile launch completion time is established. The missile launch sequence planning algorithm based on graph neural network model is designed, and the missile launch sequence is optimized locally based on node sampling and greedy insertion strategy, which can help battlefield commanders to quickly generate the missile launch sequence plan. Verification and analysis are carried out for the coordinated launch of 20-200 missiles. The experimental results show that the model and method can effectively solve the problem of temporal planning for coordinated launch of multiple missiles.

Key words: cruise missile, launch temporal planning, graph neural network, local optimization

中图分类号:

TP391

陈凯, 张德平. 基于图神经网络的导弹时序规划方法[J]. 系统工程与电子技术, 2025, 47(3): 862-870.

Kai CHEN, Deping ZHANG. Missile temporal planning method based on graph neural network[J]. Systems Engineering and Electronics, 2025, 47(3): 862-870.

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参数	参数意义
M	导弹集合, 且i∈{1, 2, …, M}
U	一个足够大的正整数
L_i	第i枚导弹最早允许飞抵初航点的时刻
R_i	第i枚导弹最晚必须飞抵初航点的时刻
C_i	第i枚导弹到达初航点的飞行耗时
S_ij	第j枚导弹后于第i枚导弹发射的最小安全时间间隔
zL	第1枚导弹飞抵初航点后，后续所有导弹必须全部飞抵各自初航点的总耗时
T_i	第i枚导弹的发射时刻
b_ij	值为1时, 表示第i枚导弹在第j枚导弹之前发射, 否则值为0
$\widetilde{u}$	所有导弹最早发射时刻
$\widetilde{\mathcal{V}}$	所有导弹最晚发射时刻
u	所有导弹最早飞抵初航点的时刻
v	所有导弹最晚飞抵初航点的时刻

模型	导弹数量
模型	20	40	60	80	100
CPLEX	310.39	345.88	360.75	369.50	374.45
GAPN-G	313.51	350.40	366.98	388.93	472.40
GAPN-SI5	313.57	353.84	370.32	384.30	394.12
GAPN-SI20	311.29	349.94	366.04	376.79	383.91

模型	导弹数量
模型	20	40	60	80	100
CPLEX	0.17	0.53	1.52	4.46	14.38
GAPN-G	0.18	0.38	0.62	0.97	1.39
GAPN-SI5	2.32	6.12	14.29	25.55	37.43
GAPN-SI20	4.85	12.46	27.15	47.48	74.45

导弹数量	评价指标	模型
导弹数量	评价指标	CPLEX	GAPN-SI5
160	$\overline{{\rm{QF}}}$	415.13	412.23
	Time	329.62	62.40
	Acc	100.00	100.00
200	$\overline{{\rm{QF}}}$	528.89	437.00
	Time	417.74	100.52
	Acc	84.00	100.00

节点数量	导弹数量
节点数量	20	40	60	80	100
1	314.80	352.68	370.46	392.66	471.41
2	314.72	353.43	372.29	394.83	470.92
4	314.23	351.57	368.27	390.37	472.22
8	313.64	350.40	366.98	389.01	472.23